It is important to remember that this section of the play comes very early on in the action, and is in fact the first time we have been introduced to both Prospero and Miranda. Because of this, Shakespeare spends significant time in this scene filling both Miranda, and us as the audience, in on the past of Prospero and his daughter and how they came to be on the island by themselves. That Miranda compares her memories to a dream rather than anything more concrete serves to emphasise how long ago it was that she was brought to the island. Note the full quotation she gives us:
'Tis far off,
And rather like a dream than an assurance
That my remembrance warrants. Had I not
Four or five women once that tended me?
That she compares her memories to a dream and is so vague about what she can actually remember or not, needing to clarify certain points with her father, indicates to us that she was brought to the island a very long time ago, so long ago as to make her unsure of her earliest memories and if they actually happened or not.